Lecture 10 - LUISS

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Lecture 10 - LUISS Powered By Docstoc
					Microeconomics
     Corso E




   John Hey
       Summary of Chapter 8
• The contract curve shows the allocations that
  are efficient in the sense of Pareto.
• There always exist the possibility of mutually
  advantageous exchange if preferences are
  different and/or endowments are different
  (unless the endowment point is on the contract
  curve).
• Perfect competitive equilibrium (with both
  individuals taking the price as given) always
  leads to a Pareto efficient allocation.
• If one of the individuals chooses the price the
  allocation is not Pareto efficient.
The competitive equilibrium depends on the
     preferences and the endowments.
• If one individual changes his or her
  preferences in such a way that he or she
  now prefers more a particular good than
  before...
• ... the relative price of that good rises.
• If an individual is endowed with more of a
  good than before...
• ... the relative price of that good falls.
          Part 1 and Part 2

• Part 1: an economy without production...
• ... just exchange



• Part 2: an economy with production...
• ... production and exchange.
                       Part 1
•   Reservation prices.
•   Indifference curves.
•   Demand and supply curves.
•   Surplus.
•   Exchange.
•   The Edgeworth Box.
•   The contract curve.
•   Competitive equilibrium.
•   Paretian efficiency and inefficiency.
                    Part 2
• Chapter 10: Technology.
• Chapter 11: Minimisation of costs and factor
  demands.
• Chapter 12: Cost curves.
• Chapter 13: Firm’s supply and profit/surplus.
• Chapter 14: The production possibility frontier.
• Chapter 15: Production and exchange.
              Chapter 10
• Firms produce...
• ...they use inputs to produce outputs.
• In general many inputs and many outputs.
• We work with a simple firm that produces
  one output with two inputs...
• ...capital and labour.
• The technology describes the possibilities
  open to the firm.
 Chapter 5                     Chapter 10
• Individuals             • Firms
• Buy goods and           • Buy inputs and
  ‘produce’ utility…        produce output…
• …depends on the         • …depends on the
  preferences…              technology…
• …which we can           • …which we can
  represent with            represent with
  indifference curves..     isoquants ..
• …in the space (q1,q2)   • …in the space (q1,q2)
         The only difference?
• We can represent preferences with a utility
  function ...
• ... but this function is not unique...
• ... because/hence we cannot measure the utility
  of an individual.
• We can represent the technology of a firm with a
  production function ...
• ... and this function is unique…
• …because we can measure the output.
               An isoquant
• In the space of the inputs (q1,q2) it is the
  locus of the points where output is
  constant.

• (An indifference curve – the locus of the
  points where the individual is indifferent.
  Or the locus of points for which the utility is
  constant.)
           Two dimensions

• The shape of the isoquants: depends on
  the substitution between the two inputs.

• The way in which the output changes form
  one isoquant to another – depends on the
  returns to scale.
       Perfect substitutes 1:1
• an isoquant: q1 + q2 = constant
• y = A(q1 + q2) constant returns to scale
• y = A(q1 + q2)0.5 decreasing returns to
  scale
• y = A(q1 + q2)2 increasing returns to scale
• y = A(q1 + q2)b returns to scale decreasing
  (b<1) increasing (b>1)
y = q1 + q2 : perfect substitutes 1:1
   and constant returns to scale
 y = (q1 + q2)2 : perfect substitutes
1:1 and increasing returns to scale
y = (q1 + q2)0.5 : perfect substitutes
1:1 and decreasing returns to scale
      Perfect Substitutes 1:a
• an isoquant: q1 + q2/a = constant

• y = A(q1 + q2/a) constant returns to scale

• y = A(q1 + q2/a)b returns to scale
  decreasing (b<1) increasing (b>1)
 Perfect Complements 1 with 1
• an isoquant: min(q1,q2) = constant

• y = A min(q1,q2) constant returns to scale

• y = A[min(q1,q2)]b returns to scale
  decreasing (b<1) increasing (b>1)
  y = min(q1, q2): Perfect
Complements 1 with 1 and
 constant returns to scale
 y = [min(q1, q2)]2 Perfect
Complements 1 with 1 and
increasing returns to scale
Y = [min(q1, q2)]0.5: Perfect
Complements 1 with 1 and
decreasing returns to scale
 Perfect Complements 1 with a
• an isoquant: min(q1,q2/a) = constant

• y = A min(q1,q2/a) constant returns to
  scale

• y = A[min(q1,q2/a)]b returns to scale
  decreasing (b<1) increasing (b>1)
y = q10.5 q20.5: Cobb-Douglas with
parameters 0.5 and 0.5 – hence
    constant returns to scale
y = q1 q2: Cobb-Douglas with
parameters 1 and 1 – hence
 increasing returns to scale
y = q10.25 q20.25: Cobb-Douglas with
parameters 0.25 and 0.25 – hence
    decreasing returns to scale
 Cobb-Douglas with parameters a
            and b
• an isoquant: q1a q2b = constant

• y = A q1a q2b

• a+b<1 decreasing returns to scale
• a+b=1 constant returns to scale
• a+b>1 increasing returns to scale
 Chapter 5                       Chapter 10
• Individuals               • Firms
• The preferences are       • The technology is
  given by indifference       given by isoquants
  curves                    • …in the space (q1,q2)
• …in the space (q1,q2)     • ..can be represented
• .. can be represented       by a production
  by a utility function u     function …
  = f(q1,q2)…                 y = f(q1,q2)…
• …which is not unique.     • … which is unique .
             Chapter 10



• Goodbye!

				
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